Example 1

Express the following in scientific notation.

1. 3,400,000

2. 0.0000008

3. 0.0047

4. 274.3

1. 3,400,000 written in scientific notation is 3.4 × 10⁶. Simply place the decimal point to get a number between 1 and 10 and then count the digits to the right of the decimal to get the power of 10.

   

   moved six digits to the left

2. 0.0000008 written in scientific notation is 8 × 10^–7.

   Simply place the decimal point to get a number between 1 and 10 and then count the digits from the original decimal point to the new one.

   

   moved seven digits to the right

3. 0.0047 written in scientific notation is 4.7 × 10^–3.

   Simply place the decimal point to get a number between 1 and 10 and then count the digits from the original decimal point to the new one.

   

   moved three digits to the right

4. 274.3 written in scientific notation is 2.743 × 10².

   Simply place the decimal point to get a number between 1 and 10 and then count the digits from the original point to the new one.

   

   moved two digits to the left

Notice that numbers greater than 1 have positive exponents when expressed in scientific notation and numbers between 0 and 1 have negative exponents when expressed in scientific notation.

Example 2

Multiply the following and express the answers in scientific notation.

1. (2 × 10²)(3 × 10⁴)

2. (6 × 10⁵)(5 × 10⁷)

3. (4 × 10^–4)(2 × 10⁵)

4. (5 × 10⁴)(9 × 10²)

5. (2 × 10²)(4 × 10⁴)(5 × 10⁶)

1. 

2. 

   This answer must be changed to scientific notation.

   Change the 30 into its scientific notation form.

   

3. 

4. 

5. 

Example 3

Divide the following and express the answers in scientific notation.

1. 

2. 

3. 

4. 

   Change 0.4 into its scientific notation form.

   

5.